Topics in the Theory of Solid Materials

Topics in the Theory of Solid Materials provides a clear and rigorous introduction to a wide selection of topics in solid materials, overlapping traditional courses in both condensed matter physics and materials science and engineering. It introduces both the continuum properties of matter, traditionally the realm of materials science courses, and the quantum mechanical properties that are usually more emphasized in solid state physics courses, and integrates them in a manner that will be of use to students of either subject. The book spans a range of basic and more advanced topics, including stress and strain, wave propagation, thermal properties, surface waves, polarons, phonons, point defects, magnetism, and charge density waves. Topics in the Theory of Solid Materials is eminently suitable for graduates and final-year undergraduates in physics, materials science, and engineering, as well as more advanced researchers in academia and industry studying solid materials.

STRAIN AND STRESS IN CONTINUOUS MEDIAIntroductionDeformation: Strain and RotationForces and StressLinear ElasticityEquilibriumWAVE PROPAGATION IN CONTINUOUS MEDIAIntroductionVector FieldsEquation of MotionWave PropagationAppendixTHERMAL PROPERTIES OF CONTINUOUS MEDIAIntroductionClassical ThermodynamicsThermal Conduction and Wave MotionWave Attenuation by Thermal ConductionSURFACE WAVESIntroductionRayleigh WavesBoundary ConditionsDispersion RelationCharacter of the Wave MotionDISLOCATIONSIntroductionDescription of DislocationsDeformation Fields of DislocationsUniform Dislocation MotionFurther Study of DislocationsCLASSICAL THEORY OF THE POLARONIntroductionEquations of MotionThe Constant-Velocity PolaronPolaron in a Magnetic Field: QuantizationATOMISTIC QUANTUM THEORY OF SOLIDSIntroductionThe HamiltonianNuclear Dynamics: The Adiabatic ApproximationThe Harmonic ApproximationPhononsStatistical Thermodynamics of a SolidSummaryPHONONSIntroductionMonatomic Linear ChainDiatomic Linear ChainLocalized Mode of a Point DefectCLASSICAL ATOMISTIC MODELING OF CRYSTALSIntroductionThe Shell Model for Insulating CrystalsCohesive Energy of a CrystalElastic ConstantsDielectric and Piezoelectric ConstantsCLASSICAL ATOMIC DIFFUSION IN SOLIDSIntroductionThe Diffusion EquationDiffusion as a Random WalkEquilibrium Distribution of Point DefectsTemperature Dependence of Diffusion: the Vineyard RelationAppendix: Stirling's FormulaPOINT DEFECTS IN CRYSTALSIntroductionClassical DiffusionDefect Complex StabilityImpurity Charge-State StabilityOptical ExcitationSpin DensitiesLocal Band-Edge ModificationElectronic LocalizationQuantum DiffusionEffective Force Constants for Local ModesSummaryAppendix: The ICECAP MethodTHEORETICAL FOUNDATIONS OF MOLECULAR CLUSTER COMPUTATIONSIntroductionHartree-Fock ApproximationThe Fock EquationLocalizing PotentialsEmbedding in a CrystalCorrelationOne-, Two-, and N-Particle Density FunctionalsPARAMAGNETISM AND DIAMAGNETISM IN THE ELECTRON GASIntroductionParamagnetism of the Electron GasDiamagnetism of the Electron GasAppendixCHARGE DENSITY WAVES IN SOLIDSIntroductionEffective Electron-Electron InteractionThe Hartree Equation: Uniform and Periodic CasesCharge Density Waves: the Mathieu EquationDiscussionReferences